We performed a deep search for radio synchrotron emissions induced by weakly interacting massive particles (WIMPs) annihilation or decay in six dwarf spheroidal (dSph) galaxies of the Local Group. Observations were conducted with the Australia Telescope Compact Array (ATCA) at 16 cm wavelength, with an rms sensitivity better than 0.05 mJy/beam in each field. In this work, we first discuss the uncertainties associated with the modeling of the expected signal, such as the shape of the dark matter (DM) profile and the dSph magnetic properties. We then investigate the possibility that point-sources detected in the proximity of the dSph optical center might be due to the emission from a DM cuspy profile. No evidence for an extended emission over a size of few arcmin (which is the DM halo size) has been detected. We present the associated bounds on the WIMP parameter space for different annihilation/decay final states and for different astrophysical assumptions. If the confinement of electrons and positrons in the dSph is such that the majority of their power is radiated within the dSph region, we obtain constraints on the WIMP annihilation rate which are well below the thermal value for masses up to few TeV. On the other hand, for conservative assumptions on the dSph magnetic properties, the bounds can be dramatically relaxed. We show however that, within the next 10 years and regardless of the astrophysical assumptions, it will be possible to progressively close in on the full parameter space of WIMPs by searching for radio signals in dSphs with SKA and its precursors.
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